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If I understand the question, no.

I want a smooth string of beziers with one control point each (are those 'degree 1 polynominals'?), which put together go through all the points in my list.

(_Felix 's school of dance and occult sciences, Thu 25 Jun 2009, 13:46, archived)

If it's a single control point, and you're not actually going through those,

The control points for the curves on either side of each point should form a straight line. The angle of that line is probably half way between the adjacent point lines.

Maybe.

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Bloop Fri 16 Jul, 22:10, Thu 25 Jun 2009, 13:58, archived)

So, they lie somewhere on some line with that angle. :)

Progress!

(_Felix 's school of dance and occult sciences, Thu 25 Jun 2009, 14:04, archived)

no that doesn't work for zigzags

i give up

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Bloop Fri 16 Jul, 22:10, Thu 25 Jun 2009, 14:04, archived)

Hmm, how would a zigzag go

The middle spline would have to be straight, and the other two severely hook-shaped in order to join on to it smoothly. So their control points would have to be way off to the side relative to their start and end points.

(_Felix 's school of dance and occult sciences, Thu 25 Jun 2009, 14:21, archived)